Find the area of composite polygon shown below top 110cm. Angel side 50cm. Bottom 180cm. Side 140cm
To find the area of a composite polygon, you need to break it down into simpler shapes and then calculate the area of each shape separately. In this case, the composite polygon can be divided into two parts: a trapezoid and a triangle.
1. Trapezoid:
The trapezoid is formed by the top and bottom sides, as well as the two side lengths mentioned. The formula to calculate the area of a trapezoid is:
Area = (sum of the parallel sides) * (distance between them) / 2
In this case, the sum of the parallel sides is (top + bottom) = (110cm + 180cm) = 290cm, and the distance between them is the height of the trapezoid, which is given as 50cm. Substituting these values into the formula:
Area of trapezoid = (290cm * 50cm) / 2 = 14500cm^2
2. Triangle:
The triangle is formed by the side length (140cm) and the height of the trapezoid (50cm). The formula to calculate the area of a triangle is:
Area = (base * height) / 2
In this case, the base of the triangle is the side length, which is 140cm, and the height is the same as the trapezoid's height, given as 50cm. Substituting these values:
Area of triangle = (140cm * 50cm) / 2 = 3500cm^2
3. Total area:
Finally, to find the total area of the composite polygon, you need to add the areas of the trapezoid and the triangle:
Total area = Area of trapezoid + Area of triangle
Total area = 14500cm^2 + 3500cm^2 = 18000cm^2
Therefore, the area of the composite polygon shown below top 110cm, with a side of 50cm, a bottom of 180cm, and a side of 140cm, is 18000 square centimeters.